Linear Recurring Sequences Over Zero-Sum skn-Halfrings.

Linear recurring sequences over semirings were introduced recently. In this paper, after investigating some properties on zero-sum strongly k-noetherian halfrings (briefly zero-sum SKN-halfrings), we study some properties of families of linear recurring sequences over zero-sum SKN-halfrings and relationships between families of linear recurring sequences and theirs annihilators. We also characterize the finitely generated subsemimodules of the S-semimodule of all linear recurring sequences over S. [ABSTRACT FROM AUTHOR]